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Simulating the Mechanics of Lens Accommodation via a Manual Lens Stretcher
Published on: February 23, 2018
A mathematical model for the deformation of the eyeball by an elastic band
Stephen L Keeling1, Georg Propst, Georg Stadler
1Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstrasse 36, 8010 Graz, Austria. stephen.keeling@uni-graz.at
Abstract:
In a certain kind of eye surgery, the human eyeball is deformed sustainably by the application of an elastic band. This article presents a mathematical model for the mechanics of the combined eye/band structure along with an algorithm to compute the model solutions. These predict the immediate and the lasting indentation of the eyeball. The model is derived from basic physical principles by minimizing a potential energy subject to a volume constraint. Assuming spherical symmetry, this leads to a two-point boundary-value problem for a non-linear second-order ordinary differential equation that describes the minimizing static equilibrium. By comparison with laboratory data, a preliminary validation of the model is given.
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